Question

Write the value  \[\left( \hat{ i }  \times \hat{ j }  \right) \cdot \hat{ k }  + \hat{ i }  \cdot \hat{ j }  .\]

 

Answer 1

\[\left( \hat{ i } \times \hat{ j }  \right) . \hat{ k }  + \hat{ i } . \hat{ j }  \]
\[ = \hat{ k }  .\hat{  k }  + 0\]
\[ = \left| \hat{ k }  \right|^2 + 0\]
\[ = 1^2 + 0 ( \because \left| k \right| = 1)\]
\[ = 1\]